A fourth reason: if you use something like Sphinx to autogenerate documentation from your code, then you should probably include at least a one-liner saying what each function or method does, and maybe you want to describe the parameters and the return values. (If you're using a language like Python, then of course you don't have the types of the parameters or the return values in the function definition, so you should document them.)

You form a hypothesis about the big bang happening, and you deduce that if it had happened, then you would be able to observe certain phenomena now, if only your measurements could be made precisely enough. (I'm not a physicist or an astronomer, but maybe the phenomena would involve the residual energy in the vacuum of deep space, or the distribution of certain elements in stars, or something about general relativity, or I don't know what.) When technology has improved enough, or when you have designed a careful enough experiment, you carry out your experiments and see if you observe those phenomena. If you don't see what you should, then you have to say that your hypothesized account of the big bang must be wrong.

I haven't read this book, but if you start with n sexual interactions, k of which are unsafe, and then you add m more, all of which are safe, then the fraction of unsafe sexual interactions has decreased: it's gone from k/n to k/(n+m). Therefore the risk in any particular interaction is less.

(A similar computation works even if the new interactions aren't all safe, but just more likely to be safe than the old ones.)

Of course it matters. Schools don't have an infinite amount of time: even if they follow your "fact-based" approach (whatever that means when it comes to writing or indeed any sort of art), they still need to make decisions about which facts to include. If the facts are wrong, it's easy to discount them. But if the RIAA (for example) comes up with lesson plans based on (let's assume) an accurate description of copyright law, then I would say that it's still not worth the time. Work on math, science, history, writing, music, any number of things before spending time on this.

Actually, it's only been in nearly some scifi movies.

So learn how to check your work. First, look at your answer and try to determine whether it makes sense, and then see if you made any silly algebra mistakes. Then if you're learning integration, for example, take the derivative and see if you get the original function back again. If you're learning differential equations, plug your purported solution in and see if it is actually a solution. In many situations, you have more than one method available to solve a problem, so try both and see if they produce the same thing.

In the real world you don't have a solution manual, so it's a valuable skill to be able to check your work without one. Furthermore, some students use solution manuals badly: if they don't get the right answer, they tinker with their work until their answer matches the right one, with no understanding of what they did wrong or what they did to correct it. It's a good idea to not have all of the answers available; for calculus, half seems about the right proportion.

I'm not sure what you're talking about -- mathematics is taught lots of different ways: there is no single, monolithic, method for "how math is taught."

You left out the relevant part:

Slashdot

People that post comments designed to get more karma, for example mirroring a linked article or presenting a banal groupthink opinion or lame joke, are often referred to as karma whores.

The Kindle has a web browser, albeit a primitive one.

Right, I understand this. I'm just trying to figure out where (if at all) jcr draws the line.

I'm curious: do you feel the same way about the minimum wage? Child labor laws? Requirements that new cars have seat belts and airbags? Do all of these create inefficiencies in the marketplace?